Multi-sphere approximation of real particles for DEM simulation based on a modified greedy heuristic algorithm

• We transfer the multiple spheres approximation problem to a set covering problem.
• We use a 0–1 matrix to describe the multiple spheres approximation.
• The modified heuristic greedy algorithm is applied to solve the problem in short time.
• A simply connected particle is represented with less than 60 spheres.
• The error of volume, area and moment of inertia is almost less than 3%.

In this paper, a new algorithm to approximate real particles using multiple overlapping spheres as numerical models for the discrete element method is introduced. First, we convert the issue of approximating particles with a cluster of multiple overlapping spheres to a set-covering problem. Then, we use an algorithm to solve the set-covering problem in detail. This manuscript presents three different solution schemes based on a modified greedy heuristic algorithm, namely, a body-covering scheme, a surface-covering scheme and a triangular surface-covering scheme. To evaluate the algorithm, we calculated the amount of multiple overlapping spheres, the intersection error of volume or area, the difference set error of volume or area between multiple overlapping spheres and the real particles, and the error of the moment of inertia of the multiple overlapping spheres and the real particles. The parameters used to evaluate the precision of the three different schemes indicated that all three schemes are excellent. It is understood that different schemes offer different levels of precision for different particles with different numbers of multiple spheres. Therefore, it is important to choose the scheme best suited to represent a particular objective. Besides, the computational time is considered as the efficiency of the algorithm. In general, the body-covering scheme approximates complicated particles with the fewer spheres and better accuracy, while the surface-covering scheme realizes the representation with less time for a few particles. However, if a particle is generated by fewer than several thousand triangles, the triangular surface-covering scheme may finish the approximation in shorter time and with fewer multiple spheres.

A new algorithm to approximate real particles using multiple overlapping spheres as numerical models for the discrete element method is introduced. Which can better descript any complex particles with very little spheres (about less than 100 spheres).Figure optionsDownload as PowerPoint slide